This invention relates generally to multislice computed tomography (CT) imaging apparatus and methods, and more particularly to methods and apparatus for backprojecting attenuation data acquired during a scan to form an image.
In at least one known computed tomography (CT) imaging system configuration, an x-ray source projects a fan-shaped beam which is collimated to lie within an X-Y plane of a Cartesian coordinate system and generally referred to as the xe2x80x9cimaging planexe2x80x9d. The x-ray beam passes through the object being imaged, such as a patient. The beam, after being attenuated by the object, impinges upon an array of radiation detectors. The intensity of the attenuated beam radiation received at the detector array is dependent upon the attenuation of the x-ray beam by the object. Each detector element of the array produces a separate electrical signal that is a measurement of the beam attenuation at the detector location. The attenuation measurements from all the detectors are acquired separately to produce a transmission profile.
In known third generation CT systems, the x-ray source and the detector array are rotated with a gantry within the imaging plane and around the object to be imaged so that the angle at which the x-ray beam intersects the object constantly changes. A group of x-ray attenuation measurements, i.e., projection data, from the detector array at one gantry angle is referred to as a xe2x80x9cviewxe2x80x9d. A xe2x80x9cscanxe2x80x9d of the object comprises a set of views made at different gantry angles, or view angles, during one revolution of the x-ray source and detector. In an axial scan, the projection data is processed to construct an image that corresponds to a two dimensional slice taken through the object. One method for reconstructing an image from a set of projection data is referred to in the art as the filtered back projection technique. This process converts the attenuation measurements from a scan into integers called xe2x80x9cCT numbersxe2x80x9d or xe2x80x9cHounsfield unitsxe2x80x9d, which are used to control the brightness of a corresponding pixel on a cathode ray tube display.
More specifically, and referring to FIGS. 1 and 2, one known computed tomography (CT) imaging system 10 includes a gantry 12 representative of a xe2x80x9cthird generationxe2x80x9d CT scanner. Gantry 12 has an x-ray source 14 (or more generally, a radiation source 14) that projects a beam of x-rays 16 (or more generally, a beam of radiation) toward a detector array 18 on the opposite side of gantry 12. Detector array 18 is formed by detector elements 20 which together sense the projected x-rays that pass through an object 22, for example a medical patient. Each detector element 20 produces an electrical signal that represents the intensity of an impinging x-ray beam and hence the attenuation of the beam as it passes through patient 22. During a scan to acquire x-ray projection data, gantry 12 and the components mounted thereon rotate about a center of rotation 24. Detector array 18 may be fabricated in a single slice or multislice configuration. In a multislice configuration, detector array 18 has a plurality of rows of detector elements 20, only one of which is shown in FIG. 2.
Rotation of gantry 12 and the operation of x-ray source 14 are governed by a control mechanism 26 of CT system 10. Control mechanism 26 includes an x-ray controller 28 that provides power and timing signals to x-ray source 14 and a gantry motor controller 30 that controls the rotational speed and position of gantry 12. A data acquisition system (DAS) 32 in control mechanism 26 samples analog data from detector elements 20 and converts the data to digital signals for subsequent processing. An image reconstructor 34 receives sampled and digitized x-ray data from DAS 32 and performs high speed image reconstruction. The reconstructed image is applied as an input to a computer 36 which stores the image in a mass storage device 38.
Computer 36 also receives commands and scanning parameters from an operator via console 40 that has a keyboard. An associated cathode ray tube display 42 allows the operator to observe the reconstructed image and other data from computer 36. The operator supplied commands and parameters are used by computer 36 to provide control signals and information t o DAS 32, x-ray controller 28 and gantry motor controller 30. In addition, computer 36 operates a table motor controller 44 which control s a motorized table 46 to position patient 22 in gantry 12. Particularly, table 46 moves portions of patient 22 through gantry opening 48.
In embodiments of imaging system 10 that employ detector arrays 18 having only a single row, only fan-beam backprojection is utilized for reconstruction of images.
Referring to the planar geometry of FIG. 3, the basic geometry for backprojecting a set of corrected and filtered detector samples R(xcex2i,xcex3j) for a particular pixel is shown. The pixel is located at coordinates (xk,Yl) and the gantry angle is xcex2 (for view number i). D is the distance from x-ray source 14 to isocenter 24, and xcex3 is the angle between a ray passing through isocenter 24 and a ray passing through the pixel.
Fan-beam backprojection of the detect or samples R(xcex2i,xcex3j) in one known imaging system is accomplished in three steps for each pixel. First, the value of the filtered detector pixel must be calculated for the ray passing through the pixel. The angle xcex3 is calculated, using interpolation between filtered detector samples that lie to each side of the angle xcex3 to yield a precise filtered projection value R(xcex2i,xcex3). Second, the distance L1 between x-ray source 14 and the pixel (xk,Yl) is calculated, and finally the value R(xcex2l, xcex3)/(L1)2 is calculated and added to the pixel value.
To simplify these calculations, an alternative coordinate system defined by s and t is used rather than x and y. The s axis lies a long a line from source 14 to isocenter 24 while the t axis passes through isocenter 24 at a right angle to the s axis. Thus, the s and t coordinates are simply the x and the y coordinates rotated by the gantry angle. Values for s are positive from isocenter 24 towards detector array 18 and negative from isocenter 24 towards source 14. Values for t are positive for positive xcex3 and negative for negative xcex3.
The value of xcex3 using this coordinate system is written:   γ  =                    tan                  -          1                    ⁡              (                  t                      D            +            s                          )              .  
Rarely will xcex3 exactly equal one of the discrete yj values that correspond to one of the detector samples R(xcex2i,xcex3j). Instead, xcex3 will usually lie between two xcex3j values. In this general case, linear interpolation is used to approximate the actual value of R(xcex2i,xcex3).
Using the Pythagorean theorem, the value of L is written:
L={square root over (t2+L +(D+s+L )2+L )}.
The values of xcex3 and L are calculated directly by a pipeline CORDIC processor of a type described in U.S. Pat. No. 4,896,287 and in J. E. Volder, xe2x80x9cThe CORDIC Trigometric Computing Technique,xe2x80x9d IRE Transactions on Electronic Computers, September 1959, pp. 330-334. The CORDIC (COordinate Rotation DIgital Computing) algorithm is an efficient algorithm that computes certain transcendental functions. The algorithm is time-efficient because it replaces multiplication and division operations by shift operations, leaving additions as the only costly computation. The CORDIC processor accepts and inputs two values A and B and makes the following computations:
xcex8=tanxe2x88x921(B/A);
and
r=k{square root over (A2+B2+L )};
where       k    =                  ∏                  i          =          0                          n          -          2                    ⁢              xe2x80x83            ⁢                        1          +                      2                                          -                2                            ⁢              i                                            ,
through a series of vector rotations of angle and scaling steps. By substituting pixel coordinate t for input B and the pixel coordinate D+s for input A, the CORDIC processor computes the values of xcex3 and kL directly. Inputs t and D+s are prescaled by dividing by k in one embodiment so that the desired values of xcex3 and L are directly produced. The constant k is a known constant based on a number of pipeline stages used to implement the CORDIC processor. The filtered projection data value R(xcex2i, xcex3) is then determined using xcex3, and it is divided by L2 to produce the amount added to the pixel value. Each acquired view during the scan is backprojected in this manner to each pixel in the 2D image being reconstructed.
Referring to FIGS. 1, 2, 3, and 4, during a scan, a series of views (xcex2i) of patient 22 is acquired as gantry 12 rotates around an axis that passes through isocenter 24. Each view of scan data is received from DAS 32 and further processed in image reconstructor 34. Details of the additional processing are shown in to FIG. 4. More particularly, each view of scan data is received from DAS 32 and further processed 50 to correct for various well-known errors such as variations in detector and channel gains. The corrected data is log adjusted 52 by taking the negative of its logarithm to provide a projection profile that indicates the amount of attenuating material in patient 22 along the x-ray beam associated with each detector element 20. The projection profile is then filtered 54 by convolving it with a reconstruction filter kernel in preparation for backprojection.
Each filtered projection profile R(xcex2i,xcex3j) is applied to a backprojector 56 that stores these values in a projection memory 58. Backprojector 56 determines from the filtered projection profile R(xcex2i,xcex3j) what values must be added to each pixel (x,y) in a slice image 60 being reconstructed in memory. A controller 62 operates backprojector 56 by outputting the coordinates (in this case, the x and y dimensions) of the pixel to be updated at 64 and by outputting corresponding values t/k and (D+s)/k for this pixel into a CORDIC processor 66 that produces an angle xcex3 and distance L of each pixel location from x-ray source 14. The value of xcex3 is used to read two adjacent values from the filtered projection 58. These two values are applied to an interpolator 68 to linearly interpolate between the two values to produce the filtered backprojection value R(xcex2i,xcex3) for a ray through the pixel x,y.
The value of L produced by the CORDIC processor 60 is squared in a multiplier 70 and applied to a divider 72 that divides the filter projection value R(xcex2i,xcex3) by the distance squared of the pixel from x-ray source 14 (L2). Controller 62 repeats this backprojection process for each pixel in slice image 60 to completely backproject the filtered projection data for one view. The next view is then applied to backprojector 56 and the process repeats to update each pixel value in slice image 60 with the contribution from this view. When all views have been acquired and backprojected, slice image 60 accurately depicts a view in cross-section taken through patient 22 in the plane of x-ray fan beam 16.
The above-described prior art embodiment is useful for single-slice systems in which fan-beam backprojection is utilized for reproduction. Known embodiments of imaging system 10 that employ a multislice detector array 18 also employ only fan-bean backprojection for reconstruction. However, to produce better quality images, it would be desirable to efficiently take into account the additional dimension across detector rows. It would also be desirable to render three-dimensional images with greater precision than is possible when using fan-beam backprojection for reconstruction.
There is therefore provided, in one embodiment of the present invention, a method for reconstructing a volume image of an object. The method includes steps of scanning an object with a multislice computed tomographic (CT) imaging system having a multislice detector array to acquire projection data of a volume of the object; filtering the acquired projection data; and backprojecting the filtered projection data to reconstruct voxels of the volume image. The multislice detector array has a plurality of rows and columns of detector elements and the backprojecting includes interpolating the filtered projection data across both rows and columns of the multislice detector array.
Embodiments of the present invention, such as the embodiment described above, produce improved image quality by efficiently taking into account the additional dimension across detector rows. Three-dimensional images are rendered with greater precision than is possible when using fan-beam backprojection for reconstruction.